"Missing return type on function" for every React class method

I just got it working by adding the rule into .eslintrc.json with

{ "allowTypedFunctionExpressions": true }

.eslintrc.json

{
  "parser": "@typescript-eslint/parser",
  "extends": ["plugin:@typescript-eslint/recommended"],
  "plugins": ["@typescript-eslint"],
  "rules": {
    "@typescript-eslint/explicit-function-return-type": [
      "error",
      { "allowTypedFunctionExpressions": true }
    ]
  }
}

versions

"@typescript-eslint/eslint-plugin": "^1.10.2",
"@typescript-eslint/parser": "^1.10.2",
"eslint": "^6.0.0",

Try writing the return type for render function as

render(): JSX.Element {
  // render code
}

This works for me!